The Senator's Dilemma

What game theory can teach us about the fate of health care reform.

The Senate likes to think of itself as the world's greatest deliberative body. But there's a less charitable way to think about it: It's the world's greatest collective-action problem.

Passing health care reform has been the Democrats' worst nightmare, but it's a game theorist's dream. The dilemma is simple. The worst-case scenario for Democrats as a whole is to pass no health care bill at all. (Both chambers have already voted in favor of health care reform, so Democrats have spent political capital without anything to show for it.) And yet some individual Democrats oppose moving forward with the bill. And Republicans, of course, have many reasons to oppose it on both individual and collective grounds: They may disagree with its proposals, and, politically, they have no incentive to join the opposition.

It turns out the dilemma facing Democrats reflects a classic model in game theory, explained Kevin Morrison, a professor who teaches game theory at Cornell University. Or, rather, two classic models, depending how you look at it. The first is the "prisoner's dilemma," the other is a model called "the battle of the sexes." The prisoner's dilemma imagines two prisoners locked in separate cells. If both deny committing a crime, they both go free. If one cooperates and the other denies, the one who cooperates goes free and the other gets locked away. If they both confess, they're both screwed. In other words, it's in their collective interest to deny but in their individual interests to cooperate.

The political equivalent is that when all other Democrats are voting for health care reform, it's in an individual Democrat's interest to oppose it. And not just for ideological reasons. By holding out, he or she can extract concessions in exchange for his or her support. If the whole thing collapses, that's bad for the Democrat in the end. But short-term calculus suggests he or she should oppose it.

There are two ways to solve this kind of problem, Morrison explained: Change the payoff system or promise to return the favor later. Changing the payoffs basically means adding incentives to cooperate. Hence the "cornhusker kickback" Sen. Ben Nelson was able to extract for Nebraska and the "Louisiana purchase" Sen. Mary Landrieu got for her state. Future promises work in repetitive systems, where similar dilemmas come up again. The Senate is a perfect example. If Nelson supports health care reform, for example, Majority Leader Harry Reid will be sure to prioritize Nelson's pet legislation next time around.

Adding Republicans to the mix complicates things a bit. Republicans don't benefit politically if the bill passes (in the sense that their party won't get credit for it). But the model remains essentially the same. Republicans just require even greater payoffs to make it worth their while. According to this model, Democrats would simply have to make Olympia Snowe or Susan Collins or Scott Brown an offer they can't refuse. These deal-sweeteners—some might call them bribes—could backfire as they did with Nelson. But they could still work.

The "battle of the sexes" model is slightly different. The premise is that a couple wants to spend a night out. But they want to do different things. The man wants to go to a football game. The woman wants to go to the opera (or the reverse, if you prefer). But more than anything, they want to spend the evening together. It's therefore in their interest to cooperate, even though whatever they decide will be one person's second choice. It's also to each person's advantage to go first—to signal that they're determined to go to the football game, say, so the other person is forced to come along.

Democrats mirror this model in that they all want health care reform—they just want different versions of it. They also can't agree on how to pass it. Does the House want to pass the Senate version? Do they want to use the reconciliation process to push through the budgetary aspects of the bill? Or do they want to start from scratch and work with Republicans? In this scenario, President Obama would theoretically signal that he wants to go one way, and Democrats, who want something, anything, passed, would be forced to follow. But he hasn't done that.

Again, the model is oversimplified. The fact that the Republicans have veto power means that Democrats have to do more than just agree among themselves. And the assumption that all Democrats agree that any bill is better than no bill may be off, too. (Clearly, some would be happier with nothing at all.) But the central problem—the interests of individual Democrats trumping the collective interests—remains.

This fact isn't true of the health care debate alone. Congress is designed to create collective action problems. It's a structurally "indecisive" body, says Alvin Roth, an economics professor at Harvard University who teaches game theory. And not just because of the filibuster. By requiring a majority (at least) in two separate chambers to pass legislation, the founders created a situation in which most members of Congress can favor a bill but it still gets blocked. "They set us up for not passing laws," Roth says.

That doesn't mean the Founders didn't want health care reform to pass. It just means they intended it to be a pain in the ass.